Lenses on very curved zones of a singular foliation of \(\mathbb{C}^2\). (English) Zbl 1441.14097
The authors renormalize, using suitable lenses, small domains of a singular holomorphic foliation of \(\mathbb{C}^2\) where the curvature is concentrated. At a proper scale, the leaves are almost translates of a graph that the authors call profile. When the leaves of the foliations are levels \(f =\lambda\), where \(f\) is a polynomial in \(2\) variables, this graph is polynomial. They also indicate in this paper how their methods may be adapted to study \(3\) levels of polynomials and 1-forms in \(\mathbb{C}^{3}\).
Reviewer: Nivaldo de Góes Grulha jun. (São Carlos)
MSC:
| 14H20 | Singularities of curves, local rings |
| 14B05 | Singularities in algebraic geometry |
| 53C65 | Integral geometry |
| 53C12 | Foliations (differential geometric aspects) |
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